Stirling Engine Thermodynamics

[matt brown]

Heat conversion to work, or kinetic energy transfer as "work" input or output is instantaneous. Like one billiard ball smacking into another, the motion is transferred from one to the other instantaneously. Heat transfer is slow as molasses.

It's commonly assumed that gas speed equals the speed of sound, so about 760 mph or 1100ft/sec. An adiabatic process is fast due to particle collision frequency which varies easily with 3D variation. However, something like simple heating can be misleading. A crude ECE isothermal process is slow due to 2 obvious issues: (1) heat source area to gas volume (2) the temperature difference between source and gas. However, the heat source metal (assuming old world ECE) is far denser than gas, so the hit ratio (gas to source metal) is far greater than between gas particles. The often overlooked boogaboo here is that a boundary layer of working gas on source slows the 'bucket brigade' from spreading heat thru gas (soup gets hot faster when you stir it, wind chill on exposed skin, etc). Over the years, I've seen some amusing source & sink schemes like forcing the working gas thru a liquid, and various 'seeding' schemes.

My favorite ECE remains Otto cycle, but allow that Stirling or others might make it for utility scale power plant with geothermal or solar.

[matt brown]

So, with heat conversion to work output, there is no need to remove the heat to a sink, in fact it's impossible, as it has already gone out as work.

But Tom, a real Stirling has another sink, aka a regenerator; it's just an internal sink vs conventional external sink. Also, an isothermal compression can be viewed 2 ways (1) globally where no heat is compressed out of working gas, but the heat of compression dissipates as heat (2) locally where, in very small steps, adiabatic compression precedes isochoric cooling. Overall, it doesn't matter, since both have no net heat compressed out of the working gas, no change in internal energy, no change in temperature. The compression heat sink in a Stirling is not to remove heat from the working gas (everything is already at lowest energy level in cycle) but to prevent heat from entering the cycle (at this time) due to compression work. This heat loss (sink) during compression is not as bad as it seems, since it reduces Wneg of compression vs adiabatic compression AND (ideally) maintains minimal temperature of cycle whereby maximum regen is possible. Nixing isothermal compression largely nixes regen potential. Isothermal compression games all work can become heat, wherein (ideally) all compression work dissipates the least heat for the least work of a compression process at the lowest energy level of the cycle.

Soapbox mode on: you guys have to get beyond PVT (pressure-volume-temperature) which might be easy to measure, but don't tell the real story. PVT values are like symptoms for a disease, just symptoms !!! This is really about energy where some stuff is intuitive, but some stuff remains counter-intuitive. Staying with an isothermal process, it's secondary that volume is inverse pressure. What's primary is that an isothermal process has constant internal energy and that internal energy is directly linear absolute temperature. So, an isothermal volume could expand 'forever' and the pressure 'disappear', but as long as it keeps its temperature, each gas particle has the same speed and the same internal energy, tho the volume will be so big, and the pressure so low, that no one will notice and no one could use it for anything.

[VincentG]

Matt, it sounds to me that you are describing Tesla's earthquake machine. And unless one of us has the brilliant spark of Tesla, we are stuck driving a piston with pressure gained from temperature. I notice as I type this that a google bot is active on the forum. Maybe we can have chat gpt solve this problem for us.

Back to a more reasonable reality, the Mod II automotive Stirling engine back in 1986 had enough power density to go in a 3000lb car with a manual transmission.

Imagine a modern version able to run at continuous optimum rpm in a hybrid drivetrain, all while powered by a small pellet stove in your trunk.

I realize the point of this thread is to understand the thermodynamics of the SE, but perhaps we are better served to perfect the tech we have at our disposal today. As opposed to theorizing an ideal that no one as of yet(that we know of) has devised.

I own a very capable desktop cnc machine, akin to what MANY others in my age group own or have access to. The age of the home machine shop and additive manufacturing has never been better for small scale production.

So I ask you Matt, with all the research you have done, what known iteration of the closed Stirling cycle do you think has the most potential?

[Tom Booth]

So, with heat conversion to work output, there is no need to remove the heat to a sink, in fact it's impossible, as it has already gone out as work.

But Tom, a real Stirling has another sink, aka a regenerator; it's just an internal sink vs conventional external sink. (...)

Well, ok, lets think about this in terms of "Carnot efficiency" and what I actually have on hand for testing: my model LTD engines.

Taking the formula Efficiency = TH−TC/TH and plugging in the values, being overly generous in terms of maximum possible efficiency we get 300 - 295/300 or about 20% efficiency.

So we let say 1000 joules of heat into the engine the first cycle 200 joules are converted to power output, 800 get stored in the regenerator.

Next cycle?

Another1000 joules added? Maybe we take 100 joules from the heat input and 100 from the stored heat in the regenerator, so now we have 900 joules of waste heat.

Regenerator or no regenerator, at 20% efficiency the "waste heat" is going to accumulate to the point of overflowing very quickly. In theory (Carnot limit [or "LAW"] that is) that excess waste heat will have to be dumped to the sink sooner or later or the heat will back up and cause the engine to overheat and stall.

None of this seems to square with the actual experimental results. i.e. the cold side of my 20% efficient engine remaining at room temperature (or just below room temperature) and running for hours and hours on end, with or without a regenerator, with the cold side open to the air or smothered with insulation.

A regenerator (a wad of steel wool or some lamp pull chain in this case) cannot just absorb an infinite amount of "waste heat" forever, so that it never becomes detectable at the "sink".

[matt brown]

Tom, you have the Carnot equation wrong, but you'll love your error !!! Carnot eq. is eff=(Th-Tc)/Th such that eff=.02 when Th=300 and Tc=294. Now, what you're getting at is an even bigger issue: if 2% goes to work then 98% goes to sink, and engine should (will for Carnot fanboys) sink nearly as much heat as source is supplying. I'll go along with this and suggest how this is possible. The total amount of work any LTD does is tiny, so both input and output (via Carnot) are tiny, it's just the ratio (50:1) that's insane. Kolin came up with the LTD as a teaching model similar the Rubik's cube, but it was Senft that 'optimized' the scheme into the hand held model. Oh yeah, this is a scheme, and almost a scam, since it's a misdirection of thermo like a magician's illusion. I think Senft wasted years tinkering with LTD that could have been better spent. Returning to LTD, once we find sink nearly equals source, the game becomes how did Senft kept LTD running without stalling from overheating AND within an acceptable range of values for homies. Yep, Senft went "where no one had gone before" and made this bugger famous. My recent deep dive into moisture issue for air compressors makes me think Senft was gaming moisture content of air. An interesting experiment would be how LTD perform on other gases.

[Tom Booth]

Tom, you have the Carnot equation wrong, ...

The equation isn't wrong, but the value of 300°k for the hot side was a mistake.

That should have been the temperature of the hot water, just boiled in the microwave.

That should have been more like 360° or up to 370°k just under boiling.

The 20% Carnot efficiency is probably being overly generous anyway.

The room about 68°F ambient, the water about 200°F

Though it's true some LTD engines could run on a 6° ∆T that was not the case in my experiments.

[matt brown]

Carnot Eq..png (152.12 KiB) Viewed 10002 times

Tom, I botched my OP and scrambled to edit before timing out. There's several flavors of Carnot equation which easily adds to confusion. Attachment has old form which I finally used with minor mod of your values. Note via this version, eff=(Th-Tc)/Th or when Th=300 and Tc=294 then eff=(300-294)/300 or eff=6/300 or eff=.02 per my current edit.

[Tom Booth]

Carnot Eq..png

Tom, I botched my OP and scrambled to edit before timing out. There's several flavors of Carnot equation which easily adds to confusion. Attachment has old form which I finally used with minor mod of your values. Note via this version, eff=(Th-Tc)/Th or when Th=300 and Tc=294 then eff=(300-294)/300 or eff=6/300 or eff=.02 per my current edit.

Well, as I said, maybe we cross posted, but that should have been around 360°K not 300 but anyway, aside from that not panning out experimentally, it makes no sense however you slice it IMO.

Take a "pancake" LTD with a huge surface area and minimal volume, vs. A "high temperature" engine with a very small surface area.

You can get just as many joules of actual heat into the LTD at a much smaller ∆T due to the larger surface area. That the temperature difference magically has some bearing on engine efficiency is just hogwash. Just left over nonsense from when heat was considered some kind of fluid falling down like a waterfall from a higher to a lower temperature.

To say:

if 2% goes to work then 98% goes to sink, and engine should (will for Carnot fanboys) sink nearly as much heat as source is supplying. I'll go along with this and suggest how this is possible. The total amount of work any LTD does is tiny, so both input and output (via Carnot) are tiny

,

Is just a silly side stepping of the issue with a completely illogical argument.

The less work the engine does, the less heat is converted to work, that does not make for less ("tiny") waste heat it means MORE waste heat.

Whatever is not converted to work output has to be "rejected" as waste heat, so this "tiny" amount of work argument is as bogus as the rest of the whole Carnot limit proposition.

[matt brown]

Now I see .20 eff from 360k, but agree that .20 from 360k gives Carnot too much credit. Another key takeaway here is that source temperature is irrelevant with Carnot buzz, it's Th of gas that counts. So, it's often possible that a range of inputs will roughly yield the same engine results, except mainly cycle rate (rpm).

I think LTD approximate an Otto cycle where 'approximate' results from out-of-phase gas dynamics. One of the most interesting aspects of an Otto cycle is that source & sink values are fairly independent of engine issues. Yes, source must be higher than temperature of working gas after adiabatic compression, and sink must be lower than temperature of working gas after adiabatic expansion, but Th of working gas is mostly constrained by just source temperature. The basic Otto is a simple gas spring with heating at one end and cooling at the other end. This is why a crappy lawnmower can spit & sputter, but still crudely run.

Imagine a magical LTD with discontinuous motion wherein start position has 'power' piston locked 'in' while displacer is against cold plate, but free to move (I'm avoiding using TDC & BDC). Moving displacer to hot plate will displace working gas to cold plate. Now lock displacer and unlock piston and piston will move 'out'. This is an Otto cycle where the only cooling should be after the piston is 'out', so a "cold plate" is probably more of a heat source short during displacement than a heat sink during compression. If the power cylinder (I almost gag calling it such) had a greater surface area to volume ratio (and was highly conductive) I doubt the cold plate would be necessary. But maybe it's due to goofy phasing or the relatively high source temperature potential vs meager volume differential. One thing I know is that the volume ratio of the 'power cylinder' to overall volume must very low...just try adding a larger piston/cylinder sometime.

[matt brown]

So I ask you Matt, with all the research you have done, what known iteration of the closed Stirling cycle do you think has the most potential?

Forget all the regen cycles: Stirling, Ericsson, Brayton, whatever, and leave them for utility scale power plants. This will likely happen, but not in my lifetime (maybe yours) and, I suspect, be the last use of classical thermodynamics.

Meanwhile, for distributed power (especially DIY) I think closed Otto cycle is the best option. Atkinson is another contender with efficiency between Otto and Stirling, but closed Atkinson cycle is not flexible. As per another recent post of mine (regarding LTD) an Otto cycle has source largely independent of engine. IOW, Otto eff is related to compression ratio, and since Otto is little more than a gas spring with heating at one end and cooling at the other end, you can add input to increase power or lessen input to decrease power...as longer as you source temperature remains above temperature after adiabatic compression.

Most of my schemes involve piston-cylinder-crank stuff and often repurpose ICE & compressor parts (why reinvent the wheel). The beauty of the piston/cylinder is that the side seal & end seal are one: the rings, unlike rotary stuff like a Wankel or vane pump. Another Otto advantage is that the engine itself is insulated, so it's possible to recycle an air or water cooled block. I think your hot bulb is a good start, since the ports allow an open cycle to get it working, then you can always pressurize by porting intake & exhaust to cooling reservoir. OK, no rocket science yet, and rigged with 6:1 compression for air, your scheme has (ideally) a 300k>>>600k adiabatic compression. Now, all you have to due, is...somehow...get some heat into the air with a source increasing air temp beyond 600k. The more heat you can get in, the more power per stroke AND the more rpm. And to think, all this possible with an ICE mindset and NO goofy ass phasing, regen, etc Stirling issues !!! Now for the bad news, but the only bad news: with an ICE conversion, just how do you get the heat in ??? Obviously, there's no change of sufficient dwell at TDC to allow source input (akin fantasy Stirling isothermal input), so where's the hat trick hiding ???

I spent decades pondering Otto ECE and have split the options into 4 flavors:

(1) single cylinder with input in head
(2) single cylinder with valve to input reservoir
(3) two cylinder with input between cylinders (aka split cycle these days)
(4) multi cylinder gas circuit

The patent office is loaded with #1 schemes and this remains the dominant fantasy. A few years, I came up with another contender, but still consider it half-baked (maybe a 'few more years'). My recent pinwheel scheme is #2 and nearly practical since it solves common piston/cylinder volume to reservoir at TDC. If #2 was conv'l piston/cylinder to reservoir (think ICE with magic valve thru spark plug hole to reservoir) this ain't gonna happen, since at soon as magic valve connects reservoir, the cylinder gas volume does not exchange with hotter...higher pressured...reservoir volume. No way, Jose. Instead, the higher reservoir pressure merely allows...some...reservoir gas to enter cylinder, and there's no constant volume ('swap') happening, and everything slows down, quickly (and stalls). Meanwhile #3 appears easily possible but not as sweet as it appears (only a deep dive will reveal it's shortcomings). I included #4 because it's possible, but nearly crazy.

[matt brown]

Yikes, I forgot another nasty of #2. The 'constant volume' transfer between cylinder and reservoir hinges on same gas mass being transferred (more or less) continuously. This means, to borrow a steam term, that the valve action from reservoir to cylinder must function as a cutoff valve. If you refer back to my pinwheel sketch, the compression volume exits the rotor via an annular port 'opening' at 11:30 while the expansion volume enters the rotor via an annular port 'closing' at 12:30. This could be one large port, but probably better as separate ports. The important thing is the 11:30 port can be fixed or variable, but the 12:30 port will need to be variable (a crude setup might be single adjustable port that functions like an advance/retard switch). Nevertheless, this mass balance issue is what has nixed many 'reservoir' schemes, some that were credible, but too finicky to pursue. Just google 1919 Stoddard engine patent to see a famous reservoir scheme that many have reinvented, but no one has made work, and few guys know why...

[matt brown]

Another reason to avoid the Stirling cycle is the pressure 'flutter' (rise and drop between blows) during regen. 20 years ago, I solved the conventional phasing issue by luck, but hit the wall when it came to regen. Yep, I mooched some ICE magic and solved the conv'l Stirling issue, but got bogged down by regen issues since. Yep, my magic widget could run all the major cycles with various compression ratios, but simply choked on regen when high compression. So, I sat on this one (like others) until I finally solved the problem early last year. Oddly, I used the same ICE magic to solve my regen problem as the widget itself uses, just in a different context. If you guys saw my widget, then my regen issue, then my solution, you'd send me off to an island to live it out with Wilson. My only defense for missing the 'obvious' is that regen cycles rarely excite me, and I had better ways to chase Otto. This widget would make an xlnt Stirling, but more likely utility only similar the geothermal thermal plants at the Salton Sea (SoCal 'lake') where one has a megabuck ECE with 2.5 minute cycle rate (how's that for slooooow isothermal input).

Meanwhile, after I solved my widget's regen problem, I saw that a similar trick could be used on a simpler design, albeit less output and less eff, but very simple and...recognizable...in the ECE world. So, my widget design is a little twisted, but this later 'design' (if I can even claim it as a design) is real mainstream, exactly what you'd expect a DIY ECE to look like. It's very similar to Watt popping a condenser on a steam engine and reinventing the steam engine. I'm designing one of these now where the crucial part is a legendary ICE part, just so everyone gets the 'gimmick'. All I'll say for now is that it's a rehash of a famous 600k ECE and I might drop in on "that guy in New Hampshire".

But wait, there's more...along the way, I somehow solved the Ericsson riddle. Tom appears to be right and Carnot limit is bogus. My previously mentioned widget came from 'misreading' an e-waste recycling flowchart as a gas circuit and a weird freeway headtrip (can't say more or it might expose the 'magic') while this eureka moment came from late night doodling while falling asleep (chalk this up to common altered state). OK, Ericsson choked, but no one has figured out this twist ??? The good news it beats Carnot, the bad news is relatively low powered cycle.

It makes me wonder if Uncle Sugar already knows all this (and more) and simply keeps it locked up until 'needed'. So, the answers are out there, they're just few and far between, and all the low hanging fruit is gone.

[Tom Booth]

.... Tom appears to be right and Carnot limit is bogus.

You've gone and done it now Matt.

Now Google, YouTube, Facebook and Twitter will flag the forum for spreading misinformation.

[matt brown]

Good one Tom, we might have to hide in the basement.

With fresh eyes, I need to add a few things to my recent engine schemes:

(1) The 'widget' started out to nix conv'l phasing issues AND provide higher compression ratio than common 2:1 of most comm'l Stirlings. For many years I was blinded from regen flutter issue (pressure swings between blows) and had I known this nearly obvious issue when I started, then I probably never would have pursued this widget. Anyways, my idea was that the higher the compression ratio, the more power per stroke for each regen 'blow'. Thus, for any given regen inefficiency, the total system efficiency would increase simply by increasing the compression ratio. So, in my early days, I was chasing a solution without first quantifying what I was trying to solve. After I had the mechanical solution, I spent a lot of time trying to quantify regen load (via simple reduction) only to find that once the compression ratio exceeds about 3x the thermal ratio of the system, then regen is kinda bogus. IOW consider a system where Tr=thermal ratio, and Vr=volume ratio (better buzz than compression ratio). When Vr/Tr=3, regen doesn't matter much. If system has 600k source and 300k sink then system is Tr=2, and once Vr=6 then Vr/Tr=3, then you can kiss regen goodbye. And since I love the DIY 600k 'limit', regen didn't matter when Vr=6 or greater. So with 600k source and Vr=6, I could nix all the regen issues, but widget would still suffer from slow isothermal issues, if 'Stirling'. However, widget can run any of the major cycles, so Otto would nix slow isothermal processes, but lower system efficiency, AND raise source temperature. Occasionally you can stumble into something that keeps you running in circles.

(2) The "rehash of a famous 600k ECE" is straight forward with few options, and Stirling only. Kinda like Jim Dandy #6 without all the Rube Goldberg fanfare.

(3) The 'super Carnot' (for lack of a better term) that evolved from Ericsson riddle is an irregular cycle, but a simple cycle and a simple engine (per original doodling). I'll be pondering this one for awhile, trying to optimize concept while sweeping the web (where's this been hiding ???).

[KristofB1982]

...Less heat input will not result in more work.

I'm not suggesting less heat input at the hot end, just less heat input (from the atmosphere) at the cold end, where heat is not wanted.

Regardless of the potential torque output, actual or theoretical, it seems to me that ANY work done, no matter how small or seemingly insignificant would have to result in cooler temperatures at the unheated end of the displacer where heat is not wanted resulting in greater efficiency and possibly a gradual increase in torque as the temperature differential increases.

In other words, by making a model (or any other) Stirling Engine do some work rather than just freewheeling, more heat would be converted into work and the temperature differential would increase proportionately to the amount of work being done.

It seems very difficult to find information on this subject and it is a rather obscure point, mostly discussed in relation to liquefying gases but I've found several references I can post here:

Hello Tom,

I will try to test this. I'm working on making an electric generator with the flywheel and I will load the electric circuit. So more load should result in a colder end. I will keep you updated when I have done the tests.